The linear canonical transform describes the effect of ﬁrst-order quadratic phase optical systems on a wave ﬁeld. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, ...

A signal may have compact support, be band-limited (i.e., its Fourier transform has compact support), or neither (“unbounded”). We determine conditions for the linear canonical transform of a signal having these
properties. ...

The correlation properties of speckle ﬁelds are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized ...

Sampling a function periodically replicates its spectrum. As a bilinear function of the signal, the associated Wigner distribution function contains cross terms between the replicas. Often neglected, these cross terms ...

The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements ...

An efficient algorithm for the accurate computation of the linear canonical transform with complex transform parameters and with complex output variable is presented. Sampling issues are discussed and the requirements for ...

The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization,
sampling, ...

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave ﬁeld. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform ...

In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation
effects ...

The fractional Fourier transform (FRT) is shown to be of potential use in analyzing the motion of a surface by use of holographic interferometry. The extra degree of freedom made available by the use of the FRT allows ...

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show
that in ...

The Fourier plane encryption algorithm is subjected to a known-plaintext attack. The simulated annealing heuristic algorithm is used to estimate the key, using a known plaintext-ciphertext pair, which decrypts
the ciphertext ...

The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used
to determine ...

It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains.
A ...

The signal extraction method based on intensity measurements in two close fractional Fourier domains is examined by using the phase space formalism. The fractional order separation has a lower bound and an upper bound that ...

We demonstrate an optical system that encodes two dimensional data as different polarization states. The encrypted image is recorded using a digital holographic setup and the decryption is done numerically.

A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require ...

The number of samples required for efficient numerical simulation of wave propagation can be determined by a combination of Wigner phase-space techniques, wave energy confinement arguments, and a theorem relating
energy ...

Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [D. P. Kelly et al. Appl. Opt. 44, 2720 (2005)] it has been shown that ...

The fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the
effects ...